Lcomoment.matrix {lmomco} | R Documentation

## Compute Sample L-comoment Matrix

### Description

Compute the L-comoments from a rectangular `data.frame` contain arrays of random variables. The order of the L-comoments is specified.

### Usage

    Lcomoment.matrix(DATAFRAME,k=1)

### Arguments

`DATAFRAME` | A convential `data.frame` that is rectangular
`k` | The order of the L-comoments to compute. Default is k = 1

### Details

L-comoments are computed for each item in the `data.frame`. L-comoments of order k = 1 are means and comeans. L-coments of order k = 2 are L-scale and L-coscale values. L-comoments of order k = 3 are L-skew and L-coskews. L-comoments of order k = 4 are L-kurtosis and L-cokurtosis, and so on. The usual univariate L-moments of order k as seen from `lmom.ub` are along the diagonal. This function does not make use of `lmom.ub`. The `Lcomoment.matrix` function calls `Lcomment.Lk12` for each cell in the matrix. The L-comoment matrix for d-random variables is

mbox{boldmath $Lambda_k$} = (hat{λ}_{k[ij]})

computed over the pairs (X^{(i)},X^{(j)}) where 1 <= i <= j <= d.

### Value

An R `list` is returned.

`type` | The type of L-comoment representation in the matrix: “Lcomoments”.
`order` | The order of the matrix—specified by k in the argument list.
`matrix` | A kth order L-comoment matrix.

### Note

The function begins with a capital letter. This is intentionally done so that lower case namespace is preserved. L-comoments are new in the literature and experimental in this package. By using a capital letter now, then `lcomoment.matrix` remains an available name in future releases.

### Author(s)

W.H. Asquith

### Source

Serfling and Xiao (2006).

### References

Serfling, R., and Xiao, P., 2006, Multivariate L-moments, preprint.

### See Also

`Lcomoment.Lk12`, `Lcomoment.coefficients`, `lmom.ub`

### Examples

    D  <- data.frame(X1=rnorm(30),X2=rnorm(30),X3=rnorm(30))
    L1 <- Lcomoment.matrix(D,k=1)
    L2 <- Lcomoment.matrix(D,k=2)

[Package lmomco version 0.92 Index]